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A Noether theorem f...
A Noether theorem for stochastic operators on Schatten classes
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- Bartoszek, Krzysztof, 1984- (author)
- Uppsala universitet,Analys och sannolikhetsteori,Department of Mathematics, Uppsala University, Uppsala, Sweden
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- Bartoszek, Wojciech (author)
- Gdansk Univ Technol, Dept Probabil & Biomath, Ul Narutowicza 11-12, PL-80233 Gdansk, Poland.,Department of Probability and Biomathematics, Gdańsk University of Technology, Gdańsk, Poland
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(creator_code:org_t)
- Elsevier BV, 2017
- 2017
- English.
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In: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 452:2, s. 1395-1412
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Abstract
Subject headings
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- We show that a stochastic (Markov) operator S acting on a Schatten class C-1 satisfies the Noether condition (i.e. S' (A) = A and S' (A(2)) = A(2), where A is an element of C-infinity is a Hermitian and bounded operator on a fixed separable and complex Hilbert space (H, <.,.>)), if and only if S(E-A(G)XEA(G)) = E-A (G)S(X)E-A (G) for any state X is an element of C-1 and all Borel sets G subset of R, where E-A (G) denotes the orthogonal projection coming from the spectral resolution A = integral(sigma(A)) zE(A)(dz). Similar results are obtained for stochastic one-parameter continuous semigroups.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Schatten classes
- Markov operator
- Noether property
Publication and Content Type
- ref (subject category)
- art (subject category)
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